Toward explaining black hole entropy quantization in loop quantum gravity

TL;DR

This paper investigates the step-like behavior of black hole entropy in loop quantum gravity, reformulating the problem to better understand the origin of entropy quantization and its relation to the area spectrum.

Contribution

It introduces a path-based reformulation of the horizon state counting problem, providing insights into the origin of entropy quantization in loop quantum gravity.

Findings

Reproduces the observed entropy step-length with high accuracy

Links entropy periodicity to properties of the area spectrum

Highlights the complexity of the underlying process

Abstract

In a remarkable numerical analysis of the spectrum of states for a spherically symmetric black hole in loop quantum gravity, Corichi, Diaz-Polo and Fernandez-Borja found that the entropy of the black hole horizon increases in what resembles discrete steps as a function of area. In the present article we reformulate the combinatorial problem of counting horizon states in terms of paths through a certain space. This formulation sheds some light on the origins of this step-like behavior of the entropy. In particular, using a few extra assumptions we arrive at a formula that reproduces the observed step-length to a few tenths of a percent accuracy. However, in our reformulation the periodicity ultimately arises as a property of some complicated process, the properties of which, in turn, depend on the properties of the area spectrum in loop quantum gravity in a rather opaque way. Thus, in some sense, a deep explanation of the observed periodicity is still lacking.